Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints

2020/10/26 by Marc Finzi, Finzi, Marc, Ke Alexander Wang +3 · 6 citations
Computer Science · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Computational Physics and Python Applications #Control and Stability of Dynamical Systems #Data Analysis #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Modeling and Simulation Systems #Neural Networks and Applications #Statistics and Probability (physics.data-an) #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2010.13581

openalex publication_date 2020/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian of a system rather than the differential equations directly. While these methods encode the constraints of the systems using generalized coordinates, we show that embedding the system into Cartesian coordinates and enforcing the constraints explicitly with Lagrange multipliers dramatically simplifies the learning problem. We introduce a series of challenging chaotic and extended-body systems, including systems with N-pendulums, spring coupling, magnetic fields, rigid rotors, and gyroscopes, to push the limits of current approaches. Our experiments show that Cartesian coordinates with explicit constraints lead to a 100x improvement in accuracy and data efficiency.

Cited by

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• Floating-Base Deep Lagrangian Networks
• Uncovering Emergent Physics Representations Learned In-Context by Large Language Models
• Meta-learning Structure-Preserving Dynamics
• Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures

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